156 PARTICULAR CASES OF EQUILIBRIUM. 



we have thus 



^-k 



I A'"*' 



and therefore 



The value of the potential at I, and on the whole surface with 

 two sheets, is 



2d k 



There are evidently two other points C and C on the axis where 

 the potential has the same value, and which belong to this surface. 

 For from B to A, the potential increases from zero to infinity, and de- 

 creases from infinity to zero, from the point A to an infinite distance. 

 The distances x and x' of the points C and C' from the point A, are 

 given by the equations 



20. 



All the surfaces whose potential is greater than V t surround the 

 point A ; all those whose potential is positive and smaller than V { , 

 consist of two sheets, both of them isolated and closed ; one of them 

 outside the great lobe of the surface S f surrounds the two points A 

 and A'; the other, which is inside the small lobe S' { , merely surrounds 

 the point A'. 



169. The general equation of the lines of force 



m cos to + m' cos o>' = m' + m cos 

 becomes here 



m cos <o m' cos o>' = - m' + m cos 0, 

 or 



(31) cos >' - / 2 cos eo = i - k z cos 6. 



